Angle Types & Measures 1

Let us now look at the various types of angles and their measures.

Zero Angle

A Zero Angle forms when both the arms coincide with each other. The vertex is at the one end of both the lines. It can be thought of as the initial position of both the arms, where there has been no movement of the arms. Its measure is 0 degrees

The easiest visualization of a Zero angle is a closed book or a closed door.

Complete Angle

We saw that the most natural way to measure angular movement is to take a compete rotation about a point, as a reference unit. If one of the arms of a zero angle makes a complete turn through the exterior of the angle and coincides with the other arm again, it is called a complete angle. Its measure is 360 degrees or 2π radians.

The easiest visualization of a complete angle is a book which has been opened to its maximum where the front and the back covers touch each other.

Straight Angle

When one of the arms of a zero angle, rotates so that it reaches the exact opposite side of the first arm and becomes collinear with it, the arms form a straight angle.

It is important to understand the difference between a straight angle and a straight line. The arms of a straight angle are collinear and seem to form a straight line, with the vertex falling on the line. The straight angle has a vertex. The straight line does not.

It is also important to understand the difference between a Zero angle and a Straight angle. In the Zero angle, the vertex is at one end of the arms. In a Straight angle, the vertex lies on the line formed by the arms.

If one of the arms of a Straight Angle turns through another Straight Angle, it completes a Complete Angle. Hence it is half the Complete Angle. Its measure is 180 degrees or π radians.

Right Angle

Right angle is one of the most common angles we can find in the natural & man-made world around us. It is the easiest angle to “construct” anywhere in the world. All it requires is either a piece of paper of a thread and a piece of stone!

If you fold any sheet of paper and fold it again back on the fold, you get a right angle. If you tie the piece of stone to the end of the thread and suspend it freely, it forms a right angle with reference to any line drawn on the ground. Masons have been using this idea for building vertical walls for thousands of years.

Two lines which form a right angle are also referred to as being perpendicular to each other.

We can see that a Straight Angle is the sum of 2 Right Angles and the Complete Angle is the sum of 4 Right Angles. This can easily be seen on a floor covered with square tiles. The idea of four directions North, South, East & West is also an application of this idea in real life.

The measure of a Right Angle is 90 degrees or π/2 radians.

Euclid’s Postulate – All Right Angles are Equal

One of the postulates of Euclid was that “All Right Angles are Equal”. We can interpret it as “whichever way you form a right angle anywhere, they will all be equal”. So the right angle provides an easily accessible standard to classify angles all types of angles. We will see this in the next chapter.